次分数Brown运动一个积分泛函的中心极限定理及其应用

假设S~H是Hurst参数为0H1的次分数Brown运动.本文研究积分过程1/(η(ε))∫_0~T((S_(s+ε)~H-S_s~H)~2-ε~(2H))ds,ε0的渐近分布,其中T0,η(ε)表示一个当ε→0时的无穷小量.当0H3/4和η(ε)=ε~(2H+1/2时,本文证明了上述积分弱收敛于一个标准Brown运动B的常数倍;当H=3/4和η(ε)=ε(-logε)~1/2时,证明了存在另一标准Brown运动W,使得上述积分弱收敛于3/4W.为应用,本文利用广义二次变差建立了Ornstein-Uhlenbeck(O-U)过程X_t~H=X_0~H+ σS_t~H-β∫_0~tX_s~Hds,中参数σ0的估计量,并给出其渐近正态性.     

线性过程误差下的非参数回归模型的注记

对于非参数回归模型Yni=g(xni)+εni,1in,用一般非参数方法,定义了未知函数g(.)的估计量gn(x),当误差序列{εni,1in}为一弱平稳线性过程序列时,在一定条件下,获得了估计量gn(x)的一致强相合性.     

一类线性errors－in－variables模型的参数强相合估计及其a．s．收敛速度

本文讨论了如下一类线性ｅｒｒｏｒｓ－ｉｎ－ｖａｒｉａｂｌｅｓ模型——多元线性结构关系模型β′ｘｋ＋α＝０，ξｋ＝ｘｋ＋εｋ．｛ｋ＝１，２，…，ｎ．其中，｛ｘｋ：ｋ＝１，２，…，ｎ｝为一组ｉ．ｉ．ｄ．的ｍ维随机向量，｛εｋ：ｋ＝１，２，…，ｎ｝是ｉ．ｉ．ｄ．的随机误差，Ｅ（ε１）＝０，Ｖａｒ（ε１）＝σ２Ｉｍ．且｛ｘｋ：ｋ＝１，２，…，ｎ｝与｛εｋ：ｋ＝１，２，…，ｎ｝相互独立．在一些条件下，我们证明了估计量β，α，σ２的强相合性、唯一性，并给出了估计量的收敛速度为ｏ（ｎ－１－１ｑ），这里ｑ∈［１，２）．对于Ｅ（ｘ１）ｕ１和Ｖａｒ（ｘ１）Ｖｘ的估计也得出了同样的结果     

一、二阶矩同时估计的可容许性

考虑模型Y=(y_1,…,y_n)′=(β,…,β)′+(ε_1,…,ε_n)′=1β+ε.(1.1)此处1=(1,…,1)′;ε_1,…,ε_n 相互独立,E(ε_i)=0,E(ε_i~2)=σ~2,E(ε_i~3)=0,E(ε_i~4)=3σ~4,i=1,…,n;-∞<β<∞,0<σ<∞.鉴于 β 的最重要的估计量是观察值 Y 的线性函数,σ~2和 β~2+σ~2的最重要的估计量是 Y 的非负定二次型,在考虑 β 的估计时,首先把注意力集中在 Y 的线性函数上;在考虑σ~2或 β~2+σ~2的估计时,首先考虑 Y 的非负定二次型.参考文献[1]在一般线性模型和二次损失下,给出了回归系数的可估线性函数的估计在线性估计类中是可容许的充要条件.参考文献[2]和[3]在模型(1.1)和平方损失下给出了 σ~2的估计在非负定二次型估计类中是可容许的充要条件;而在一般线性模型和平方损失下,给出了 σ~2的估计在非负定二次型估计类中是可容许的必要条件和充分条件,给出了相当大的一类可容许估计;此外,给     

相依线性回归方程组的一种“朴实”两步估计的有效性

对于相依线性回归方程组Ｙｉ＝Ｘｉβｉ＋εｉ（ｉ＝１，２），我们提出了系数向量βｉ的一种较为简便的“朴实”的两步估计量，例如β１的估计量为β１（Ｔ）＝（Ｘ’１，Ｘ１）＾－１Ｘ‘１Ｙ１－σ１２σ２２（Ｘ’１Ｘ１）＾－１Ｘ‘１ＴＹ２。其中Σ＝（σｉｊ）的一种估计量，本文给出了Σ的一种新取法，通过均方误差矩阵的大小我们证明了这种简便两种估计有有限样本量下可优效于ＬＳ估计。     

固定设计下半参数回归模型估计的强相合性

对于半参数模型ｙｉ（Ｔ）＝βｘｉ（Ｔ）＋ｇ（ｔｉ（Ｔ））＋εｉ（Ｔ），本文综合最小二乘和一般的非参数估计方法，定义了β，ｇ的估计量βＴ，ｇＴ，在适当条件下证明了它们的强相合性，     

一种改进的半参数极大似然法估计量的渐近性质

本文研究线性回归模型, Y=β'X+∈,并假设Y可被右删失,∈的分布函 数F0未知.本文证明,在某些条件下, β的一种改进的半参数极大似然法估计量β 有相合性. 同时证明,如果F0不连续,则P{β≠βi.o.}=0.这意味着以概率为一, 当样本很大时, β=β.文献中的现有估计量未见有关于这一性质的报道.相反,包括 Buckley-James估计量及M-估计量在内的大多数的估计量,都不满足这一性质.     

一类位置不变的Pickands型估计量

当极值指标大于0时, 本文提出了一种位置不变的Pickands型估计量,证明了该估计量的强弱相合性, 给出了其渐近展式和强收敛速度,并对$k_2$的最优选择进行了讨论,最后利用自适应性方法对该估计量和其它Pickands型估计量进行随机模拟分析,比较该估计量的优越性.     

三阶非线性边值问题的奇摄动(英)

本文利用Volterra型积分算子和微分不等式技巧给出了一类三阶非线性微分方程奇摄动边值问题：εX＝f（t，x，x，ε，x（0）＝A，g（x'（0），（0），ε）＝0，h（x（1），x（1），ε）＝0解的存在性．唯一性及渐近估计．     

一类拟线性抛物方程的吸引子及其均匀化

本文讨论了δtuε-divA(x/ε，↓Δuε)-kuε=f的整体吸引子A^ε与其均匀化后的方程δtu-divA(↓Δu)-ku=f的整体吸引子A^0之间的关系，并给出了A^ε与A^0之间距离的估计。     

ON A THEOREM OF A.A. LYAPUNOV

Abstract

In this note we obtain some extensions and an approximation of the Lyapunov convexity theorem by means of the bilinear integration of a set-valued function. The integration is performed successively with respect to a non-atomic, a direct sum and a Darboux vector measure. The necessary counterexamples are provided.     

A Priori and A Posteriori: A Bootstrapping Relationship

The distinction between a priori and a posteriori knowledge has been the subject of an enormous amount of discussion, but the literature is biased against recognizing the intimate relationship between these forms of knowledge. For instance, it seems to be almost impossible to find a sample of pure a priori or a posteriori knowledge. In this paper, it will be suggested that distinguishing between a priori and a posteriori is more problematic than is often suggested, and that a priori and a posteriori resources are in fact used in parallel. We will define this relationship between a priori and a posteriori knowledge as the bootstrapping relationship. As we will see, this relationship gives us reasons to seek for an altogether novel definition of a priori and a posteriori knowledge. Specifically, we will have to analyse the relationship between a priori knowledge and a priori reasoning, and it will be suggested that the latter serves as a more promising starting point for the analysis of aprioricity. We will also analyse a number of examples from the natural sciences and consider the role of a priori reasoning in these examples. The focus of this paper is the analysis of the concepts of a priori and a posteriori knowledge rather than the epistemic domain of a posteriori and a priori justification.     

有限群的一个类函数的模构造

本文研究了有限群上的一个类函数.通过计算它和不可约特征标的内积,证明了它是特征标并且通过复群代数的中心的正则表示给出了它的一个模构造.     

A REMARK ON A BMO MARTINGALE

Let M = (Mt,Ft) be a uniformly integrable continuous martingale with MO = 0. For1 5 p < cot we setIIMllBMO. = '3p II[E[IMoo ~ MTIplFT]]'/Pll.,where the supremum is taken over all stopping times T.Set BMO. = {M: IIMllBMO. < co}. It is well known that BMO. = BMO, (VI S p 5 q).F'urthermore, all 11.llBMO. norms are equivalent andIIi ~~if;llMllBMO. = SUP T P(T < co)i'where the supremum is taken over all stopping times T satisfying P(T < co) > 0. In the laterwe shall simply …     

NAMING A COLUMN ON A SPREADSHEET

Spreadsheets use a meaningful algebra-like notation which, research suggests, can support pupils in developing an understanding of variables. This paper discusses the activity of Year 8 pupils who were taught to name a column on a spreadsheet, and who were asked to reflect upon their activity in a stimulated recall interview. More specifically, it considers the pupils' understanding of notation, such as 'A2' and 'm', which they used when constructing spreadsheet formulae. It is suggested that experience of naming columns may help pupils to develop a clearer sense of the notation as a variable, and to make links between their spreadsheet activity and use of standard algebraic notation [1].     

A new characterization of A 5

Let G be a group and τ _e (G) the set of numbers of elements of G of the same order. In this paper, by τ _e (G), we give a new characterization of A ₅, where A ₅ is the alternating group of degree 5. We get the theorem following: Theorem. Let G be a group, ${G\cong A_5}$ if and only if τ _e (G) = τ _e (A ₅) = {1, 15, 20, 24}.     

简化摩擦接触问题的对称弱超内罚间断Galerkin方法的先验和后验误差估计

本文讨论了简化摩擦接触问题的一类对称弱超内罚间断Galerkin方法.首先,在能量范数意义下得到最优先验误差估计.进一步,我们推导了一类残量型后验误差估计子,并证明了它的可靠性和有效性.